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The 3D Goddard Cumulus Ensemble model is used to simulate two convective events observed during the Tropical Rainfall Measuring Mission Large-Scale Biosphere--Atmosphere (TRMM LBA) experiment in Brazil. These two events epitomized the type of convective systems that formed in two distinctly different environments observed during TRMM LBA. The 26 January 1999 squall line formed within a sheared low-level easterly wind flow. On 23 February 1999, convection developed in weak low-level westerly flow, resulting in weakly organized, less intense convection. Initial simulations captured the basic organization and intensity of each event. However, improvements to the model resolution and microphysics produced better simulations as compared to observations. More realistic diurnal convective growth was achieved by lowering the horizontal grid spacing from 1000 to 250 m. This produced a gradual transition from shallow to deep convection that occurred over a span of hours as opposed to an abrupt appearance of deep convection. Eliminating the dry growth of graupel in the bulk microphysics scheme effectively removed the unrealistic presence of high-density ice in the simulated anvil. However, comparisons with radar reflectivity data using contoured-frequency-with-altitude diagrams (CFADs) revealed that the resulting snow contents were too large. The excessive snow was reduced primarily by lowering the collection efficiency of cloud water by snow and resulted in further agreement with the radar observations. The transfer of cloud-sized particles to precipitation-sized ice appears to be too efficient in the original scheme. Overall, these changes to the microphysics lead to more realistic precipitation ice contents in the model. However, artifacts due to the inability of the one-moment scheme to allow for size sorting, such as excessive low-level rain evaporation, were also found but could not be resolved without moving to a two-moment or bin scheme. As a result, model rainfall histograms underestimated the occurrence of high rain rates compared to radar-based histograms. Nevertheless, the improved precipitation-sized ice signature in the model simulations should lead to better latent heating retrievals as a result of both better convective--stratiform separation within the model as well as more physically realistic hydrometeor structures for radiance calculations.